Method for predicting future function values utilizing derivative samples

US 6,314,327 B1
Filed: 04/28/1998
Issued: 11/06/2001
Est. Priority Date: 04/28/1998
Status: Expired due to Term

First Claim

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1. A method for calculating a future function value associated with an object from derivative values associated with the object, to then control operation of the object, comprising the steps of:

providing a sensor coupled to the object for generating derivative values;

predetermining a sampling interval T of the derivative values;

low pass filtering the derivative values to generate a high frequency value W;

acquiring at least one function value from the sensor;

determining a value for τ

by multiplying 2*T*W, wherein 2 is a Nyquist value, and wherein τ

must always be less than one;

computing a which is the solution vector of predictor coefficients in a (N+1)×

1 size matrix in the form a=[a_k⁽⁰⁾, a₁⁽¹⁾, . . . , a_N⁽¹⁾] for use in a prediction formula, wherein the prediction coefficients are found by minimizing the integral $\int_{- 2 π TW}^{2 π TW} {\langle 1 - a_{k}^{(0)} e^{-  k ω} - \sum_{n = 1}^{N} a_{n}^{(1)}  {ω}^{-  n ω} \rangle}^{2} \partial ω$

wherein said prediction formula is in the form of $f (t) = a_{k}^{(0)} f (t - kT) + T \sum_{n = 1}^{N} a_{n}^{(1)} f^{'} (t - nT)$ wherein N=the number of data points, wherein n=an integer 1 to N, and wherein k=an integer 1≦

k≦

N used to adjust the calculated result closer to the actual result to generate a future function value f(t); and

utilizing the future function value to control operation of the object.

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Abstract

A system and method for calculating a future function value, such as velocity, for an object, from derivative values, such as acceleration, includes a sensor, such as an accelerometer, coupled to an object, such as a car. By predetermining a sampling rate of the derivative values and determining the highest frequency in the sampled signal, a set of prediction coefficients can be derived for use in a prediction formula which generates the future function value. A processor, which derives the prediction coefficients and implements the prediction formula may use the future function value to control operation of the object or a related object. By including a past function value in the prediction formula, a highly accurate future function value can be determined.

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7 Claims

1. A method for calculating a future function value associated with an object from derivative values associated with the object, to then control operation of the object, comprising the steps of:
- providing a sensor coupled to the object for generating derivative values;
  
  predetermining a sampling interval T of the derivative values;
  
  low pass filtering the derivative values to generate a high frequency value W;
  
  acquiring at least one function value from the sensor;
  
  determining a value for τ
  
  by multiplying 2*T*W, wherein 2 is a Nyquist value, and wherein τ
  
  must always be less than one;
  
  computing a which is the solution vector of predictor coefficients in a (N+1)×
  
  1 size matrix in the form a=[a_k⁽⁰⁾, a₁⁽¹⁾, . . . , a_N⁽¹⁾] for use in a prediction formula, wherein the prediction coefficients are found by minimizing the integral $\int_{- 2 π TW}^{2 π TW} {\langle 1 - a_{k}^{(0)} e^{-  k ω} - \sum_{n = 1}^{N} a_{n}^{(1)}  {ω}^{-  n ω} \rangle}^{2} \partial ω$
  
  wherein said prediction formula is in the form of $f (t) = a_{k}^{(0)} f (t - kT) + T \sum_{n = 1}^{N} a_{n}^{(1)} f^{'} (t - nT)$ wherein N=the number of data points, wherein n=an integer 1 to N, and wherein k=an integer 1≦
  
  k≦
  
  N used to adjust the calculated result closer to the actual result to generate a future function value f(t); and
  
  utilizing the future function value to control operation of the object.
- View Dependent Claims (2, 3, 4, 5, 6, 7)
- - 2. The method according to claim 1, wherein said computing step comprises the step of:
3. The method according to claim 1, wherein said computing step comprises the step of:
- computing an eigenvector associated with the smallest eigenvalue of a quadratic form expressed as the integral $\int_{- 2 π TW}^{2 π TW} {\langle 1 - a_{k}^{(0)} e^{-  k ω} - \sum_{n = 1}^{N} a_{n}^{(1)}  ω e^{-  n ω} \rangle}^{2} \partial ω .$
4. The method according to claim 1, further comprising the step of:
- correcting the predicted future function by including a current sample of the derivative generated by said sensor by utilizing the following equation $f (t) = b_{1}^{(0)} f (t - T) + T \sum_{n = 0}^{N - 1} b_{n}^{(1)} f^{'} (t - nT)$
  
  with the prediction formula, wherein the corrector coefficients, $b_{1}^{(0)}, b_{0}^{(1)}, \dots, b_{N - 1}^{(1)},$
  
  are found by minimizing the integral $\frac{1}{2 π T} \int_{- π τ}^{π τ} {\langle 1 - b_{1}^{(0)} e^{-  ω} - \sum_{n = 0}^{N - 1} b_{n}^{(1)}  ω e^{-  n ω} \rangle}^{2} \partial ω .$
5. The method according to claim 4, wherein the function value and its derivative are velocity and acceleration, respectively.
6. The method according to claim 1, further comprising the steps of;
- calculating the prediction coefficients for preselected values of τ and
  
  W; and
  
  storing the calculated prediction coefficients in a computer-readable medium.
7. The method according to claim 6, further comprising the steps ofcoupling a processor to said sensor to read the derivative and function values;
- and accessing said computer-readable medium by said processor, wherein said processor determines the future function value based upon function values and derivative values and generates an appropriate signal for control of the object.

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Current Assignee
University of Akron
Original Assignee
University of Akron
Inventors
Wu, Yan, Mugler, Dale H.
Primary Examiner(s)
Gordon, Paul P.

Application Number

US09/067,835
Time in Patent Office

1,288 Days
Field of Search

700/28, 700/40, 700/42, 700/44, 701/42, 701/45-47, 701/58, 701/60
US Class Current

700/44
CPC Class Codes

G05B 13/026 using a predictor

Method for predicting future function values utilizing derivative samples

First Claim

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Abstract

18 Citations

7 Claims

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Method for predicting future function values utilizing derivative samples

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